The complex that exists as a pair of enantiomers is

Options

A. (a) `trans-[Co(H_2NCH_2CH_2CNH_2)_2Cl_2]^(+)`
B. (b) `[Co(H_2NCH_2CH_2NH_2)_3]^(3+)`
C. (c) `[Pt(PPh_3)(Cl)(Br)(CH_3)]^(-)`
D. (d) `cis-[CoNH_3)_4Cl_2]^(+)`

Explanation

To determine which complex exists as a pair of enantiomers, we need to analyze the given options based on the criteria for optical activity and the presence of a plane of symmetry (PoS). Enantiomers are non-superimposable mirror images, and for a complex to be optically active, it must lack any symmetry elements that would make it superimposable on its mirror image.

### Step-by-Step Solution:

1. **Understanding Enantiomers**:
- Enantiomers are pairs of molecules that are mirror images of each other but cannot be superimposed. For a complex to exhibit enantiomerism, it must be optically active, meaning it does not have a plane of symmetry.

2. **Analyzing the First Option (trans-Co(en)₂Cl₂⁺)**:
- The structure of trans-Co(en)₂Cl₂⁺ can be drawn, where "en" represents ethylenediamine ligands.
- In this case, if we draw the structure, we find that there is a plane of symmetry present. Thus, this complex is not optically active and does not exist as enantiomers.

3. **Analyzing the Second Option ([Co(en)₃]³⁺)**:
- For [Co(en)₃]³⁺, we can visualize the arrangement of the ligands.
- Since the ethylenediamine ligands are arranged in a way that does not allow for a plane of symmetry, this complex is optically active. Therefore, it can exist as a pair of enantiomers.

4. **Analyzing the Third Option (Square planar Pt complex)**:
- In the square planar complex with platinum, if we draw the structure, we notice that there is a plane of symmetry present. Thus, this complex is also not optically active and does not exhibit enantiomerism.

5. **Analyzing the Fourth Option (Cobalt complex with Cl and NH₃)**:
- For the cobalt complex with Cl and NH₃, when we draw the structure, we find that there is a plane of symmetry. Therefore, this complex is not optically active and does not exist as enantiomers.

6. **Conclusion**:
- Based on the analysis, the only complex that exists as a pair of enantiomers is **[Co(en)₃]³⁺**.

### Final Answer:
The complex that exists as a pair of enantiomers is **[Co(en)₃]³⁺**.